How To Find Vertical Tangent Line

You may want to read this article first: What is a tangent line? Watch the video or continue reading below: Can’t watch the video? Click here Read: how to find vertical tangentA tangent to a curve is a line segment tangent to the curve at a point. It has the same slope as the curve at that point. One vertical tangent touches the curve at a point where the slope (slope) of the curve is infinite and unknown. On the graph, it runs parallel to the y-axis.

How to find vertical tangent

General steps to find vertical tangent in calculus and gradient of a curve:

Find the derivative of the function. The derivative (dy/dx) will give you the gradient (slope) of the curve.
Find a value of x that makes dy / dx infinite; you are looking for an infinite slope, so the vertical tangent to the curve is a vertical line at this value of x.

Vertical tangent in analytic example

Read more: how to turn on the fireplace in the apartmentExample Problem: Find the vertical tangent of the curve y = √ (x – 2).Step 1: Distinguish y = √ (x – 2). You can use your graphing calculator or do the distinction by hand (using power rule and series rule). I have differentiated the function with this online calculator (showing you the steps too!): Step 2: Find the values of x that will make dy/dx infinite. This is really where strong algebra skills come in handy, although for this example problem all you need to realize is what happens if you put “2” in the equation. jaw: put a 2 Division by zero is undefined. This means that the gradient of the curve is infinite (i.e. vertical) when x = 2. The vertical tangent to the curve is x = 2. That’s it!

Graphs & Tables

Read more: how to get bubbles out of ipad screen protector If you can’t immediately see where your function can return 0, you have two choices:

Graph the function—So you can see where the graph might have a vertical tangent. I used this handy HRW calculator to get the above graph of y = √ (x – 2). Obviously there is a vertical tangent at x = 2, although you might want to go through calculus/algebra to prove it.

Make a value table and check some value of x.

The second option can be very time consuming; Solid algebra skills (like knowing when an equation can lead to division by zero) will help you avoid having to tabulate.

Some curves will have more than one vertical tangent. Always make sure you’ve found all the values of x that make the gradient infinite. You can use graphing software to visually check the places where the gradient becomes vertical.

For more tips on where functions can return 0, see the “Guess & Check” section of the Domains and Ranges article.

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